Blind estimation method of OFDM modulation parameters

ABSTRACT

The present invention concerns a blind estimation method of at least one temporal modulation parameter of an OFDM signal, in which a plurality of demodulation attempts of said OFDM signal are carried out using a plurality of respective values of this temporal parameter and, for each demodulation attempt, a cost function representative of the entropy of the demodulated signal is calculated, the estimate of said temporal parameter then being obtained as the value of this parameter minimizing said cost function.

TECHNICAL FIELD

The present invention concerns a blind estimation method of OFDM(Orthogonal Frequency Division Multiplex) modulation parameters and moreparticularly a blind estimation method based on a criterion of minimumentropy.

STATE OF THE PRIOR ART

OFDM modulation is well known in the prior art and is employed innumerous telecommunications systems such as DVB-T, ADSL, Wi-Fi (IEEE 802a/g), WiMax (IEEE 802.16). It has the advantage of good spectralefficiency and good protection against frequency selective fading.

It will be recalled that in an OFDM system, the information symbols tobe transmitted are grouped by blocks of N symbols, where N is generallya power of 2, the OFDM symbols being obtained by carrying out a IFFT(Inverse Fast Fourier Transform) on said blocks of information symbols.Generally, a cyclic prefix is added to the start of each OFDM symbol toabsorb intersymbol interference or ISI and facilitate the equalisationat reception. The OFDM signal constituted by these OFDM symbols may ifnecessary then be frequency translated.

Generally speaking, the signal emitted by an OFDM system may berepresented in baseband by:

$\begin{matrix}{{s_{a}(t)} = {\frac{\sqrt{E}}{N}{\sum\limits_{k}{{g\left( {t - {{k\left( {N + D} \right)}T_{c}}} \right)} \cdot {\sum\limits_{n = 0}^{N - 1}{a_{k,n}{\mathbb{e}}^{{- 2}{\mathbb{i}\pi}\;\frac{n}{{NT}_{c}}{({t - {DT}_{c} - {{k{({N + D})}}T_{c}}})}}}}}}}} & (1)\end{matrix}$where E is the power of the signal, N is the number of carriers of theOFDM multiplex, a_(k,n) are the information symbols relative to theblock k, belonging to a M-ary modulation alphabet, typically BPSK, QPSKor QAM, 1/T_(c) is the flow rate of the information symbols where T_(c)is the “bribe” or “chip” time, D is the size of the cyclic prefixexpressed in number of bribes, g(t) is a shaping pulse of the OFDMsymbols having a temporal support [0,(N+D)T_(c)] intended to apodize thespectrum of the signal.

An OFDM signal is represented in a schematic manner in FIG. 1. It isconstituted of a sequence of OFDM symbols, each symbol having a totaltime (N+D)T_(c) including a useful time NT_(c) and a time guard intervalT_(prefix)=DT_(c), in which is found the cyclic prefix. It will berecalled that, in a conventional manner, the cyclic prefix is a copy ofthe end of the OFDM symbol into the guard interval. In certain OFDMsystems, the cyclic prefixes are simply omitted, in other words theuseful parts of the symbols are separated by “empty” guard intervals.This transmission technique also enables the intersymbol interference tobe eliminated but does not make the equalisation of the signal easy.

After propagation in the transmission channel, the OFDM signal receivedby the receiver may be expressed as:r _(a)(t)=h

s _(a)(t)+b(t)   (2)where h

s_(a) is the convolution between the OFDM signal emitted, s_(a)(t) isthe impulsional response of the transmission channel h(t), and b(t) is arandom function describing the noise. It will be assumed that the lengthof the impulsional response is less than the time of the guard interval,such that the intersymbol interference (ISI) may be disregarded.

FIG. 2 represents in a schematic manner the structure of an OFDMreceiver.

After demodulation if necessary in baseband, the signal received issampled in 210 at the chip frequency, then the samples are subjected toa series/parallel conversion in 220 to form blocks of N+D samples. The Dfirst samples corresponding to the guard interval are discarded and theblock of the N samples remaining corresponding to the useful part of theOFDM symbol is subjected to a FFT in 230. The demodulated symbolsobtained are then subjected to a series conversion in 240.

Finally, assuming that the receiver is correctly time and frequencysynchronised, the demodulated symbols may be expressed by:â _(k,n) =h _(n) a _(k,n) +b _(k,n)   (3)where h_(n) is a complex coefficient that depends on the impulseresponse of the transmission channel, and b_(k,n) is a random variablerepresenting a noise sample.

The correct operation of this receiver necessitates a precise temporaland frequency synchronisation. Indeed, it will be understood that anincorrect temporal synchronisation will lead to a progressive temporaldrift of the truncation window and an incorrect frequencysynchronisation, a phase rotation of the samples, may be represented bya multiplicative factor e^(2iπΔfnT) ^(c) where Δf is the frequencyoffset between the demodulation frequency of the receiver and thecarrier frequency of the OFDM multiplex.

The temporal and frequential synchronisation of the receiver isgenerally carried out by means of the acquisition of a trainingsequence.

The functioning of this detector obviously assumes that the temporalparameters of modulation of the OFDM signal are known. “Temporalparameters” is taken to mean the useful time NT_(c), the time of theguard interval DT_(c) and/or the repetition period (N+D)T_(c) of thesesymbols.

Frequently, the receiver does not know a priori the temporal parametersof OFDM modulation and has to carry out their estimation blindly.

Several methods have been proposed to estimate blindly the temporalparameters. These methods exploit the presence of the cyclic prefix inthe OFDM signal and the cyclostationarity properties that can be derivedtherefrom. The estimators proposed are based on the autocorrelationfunction of the OFDM signal. An example of such an estimation method maybe found in the article of P. Liu et al. entitled “A blindtime-parameters estimation scheme for OFDM in multi-path channel”,published in Proc. 2005 Int'l Conference on Information, Communicationsand Signal Processing, vol. 1, pp. 242-247, 23-26 Sept. 2005.

These estimation methods have however the drawback of needing to acquirea high number of OFDM symbols to perform the calculation of theautocorrelation function. Moreover, these methods do not work in thecase, set out above, where the OFDM signal does not contain cyclicprefixes.

The aim of the present invention is to propose a blind estimation methodof modulation parameters of an OFDM signal that does not have theabovementioned drawbacks.

A subsidiary aim of the present invention is to enable a temporal andfrequential synchronisation of the OFDM receiver that is rapid and doesnot require a training sequence.

DESCRIPTION OF THE INVENTION

The present invention is defined by a blind estimation method of atleast one time parameter of modulation of an OFDM signal, in which aplurality of demodulation attempts of said OFDM signal are carried outby using a plurality of respective values of this time parameter and,for each demodulation attempt, a cost function representative of theentropy of the demodulated signal is calculated, the estimate of saidtime parameter then being obtained as the value of this parameterminimising said cost function.

Preferably, the OFDM signal is demodulated in baseband by means of ademodulation frequency, then sampled at a frequency greater than theNyquist frequency to obtain a sequence of samples.

Advantageously, for each demodulation attempt, said samples are thencorrected by a dephasing factor corresponding to a frequency offsetvalue between the carrier frequency of the OFDM multiplex and thedemodulation frequency.

For each demodulation attempt, the sequence formed by the samplesthereby corrected may be amputated of a given number of its firstsamples, corresponding to a temporal offset.

For each demodulation attempt, the sequence thereby amputated may be cutup into blocks of given size. Then, each of the blocks thereby obtainedis stripped of a given number of its first samples, corresponding to anOFDM symbol prefix time, and a FFT of each of the blocks therebystripped is performed.

For each block k=0, . . . ,K−1 where K is the total number of blocks ofthe stripped sequence, the FFT may be calculated by:

${\hat{a}}_{k,n} = {\sum\limits_{p = 0}^{\beta - 1}{\rho_{p}^{k}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta}}}}$where β is the size of the amputated blocks, corresponding to an OFDMsymbol useful time, T_(e) is the sampling period, ρ_(p) ^(k) is the(p+1)^(ième) frequency corrected sample of the k^(ième) block and theâ_(k,n), k=0, . . . ,K−1, n=0, . . . ,{circumflex over (N)}−1, where{circumflex over (N)} is said useful time expressed in chip periods,form a sequence of demodulated symbols according to said demodulationattempt.

The value of said cost function may then be calculated from saidsequence of demodulated symbols.

Advantageously, said cost function is the kurtosis. In this case, thevalue of said cost function may be calculated by:

${\hat{\kappa}\left( \left\{ {\hat{a}}_{k,n} \right\} \right)} = {\frac{\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{4}}}{\left( {\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}} - 2 - \frac{{{\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{k,n} \right)^{2}}}}^{2}}{\left( {\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}}}$

Advantageously, the estimation method takes place in an iterativemanner, each iteration corresponding to a demodulation attempt by meansof a said frequency offset value, a said temporal offset value, a saidprefix time and a said useful time.

As the iterations proceed, a discrete series of frequency offset,temporal offset, prefix time and useful time values are preferably runthrough, according to a scanning algorithm, and the prefix time and/orthe useful time achieving the minimum of the cost function on saidseries is retained as estimation of the temporal parameter(s).

Said scanning algorithm may be of gradient descent type.

According to an alternative embodiment, a plurality of firstdemodulation attempts are carried out to estimate a first timeparameter, then a plurality of second demodulation attempts are carriedout to estimate a second time parameter, said second demodulationattempts using the estimate of the first time parameter to demodulatethe OFDM signal.

Advantageously, for each first demodulation attempt, the samples arecorrected by a dephasing factor corresponding to a frequency offsetvalue between the carrier frequency of the OFDM multiplex and thedemodulation frequency.

For each first demodulation attempt, the sequence thereby stripped maybe cut up after a given number of samples, said number corresponding toa given OFDM symbol useful time. A FFT is then carried out on thesamples of the sequence thereby truncated.

The FFT may be calculated by:

${\hat{a}}_{n} = {\sum\limits_{p = 0}^{\beta - 1}\;{\rho_{p}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta}}}}$where β is the length of the truncated sequence, T_(e) is the samplingperiod, ρ_(p) is the (p+1)^(ième) frequency corrected sample of thetruncated sequence, the â_(n), n=0, . . . ,{circumflex over (N)}−1,where {circumflex over (N)} is said useful time expressed in chipperiods, forming a sequence of demodulated symbols according to saidfirst demodulation attempt.

A first value (Φ(Δφ,δ,β)) of said cost function may be calculated fromsaid sequence of demodulated symbols.

Advantageously, said cost function is the kurtosis.

In this case, the value of said cost function may be calculated by:

${\hat{\kappa}\left( \left\{ {\hat{a}}_{n} \right\} \right)} = {\frac{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{4}}{\left( \;{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{2}} \right)^{2}} - 2 - \frac{{\;{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{n} \right)^{2}}}^{2}}{\left( \;{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{2}} \right)^{2}}}$

The estimation method operates advantageously in an iterative manner,each iteration corresponding to a first demodulation attempt by means ofa said frequency offset value, a said temporal offset value, a saidprefix time and a said useful time.

As the iterations proceed, a discrete series of frequency offset,temporal offset, prefix time and useful time values are preferably runthrough, according to a scanning algorithm, and the frequency offset,temporal offset and useful time values achieving the minimum of the costfunction on said series is memorised, the estimation of the first timeparameter being the useful time thereby memorised.

Each sample of said sequence of samples may be corrected by a dephasingfactor corresponding to the frequency offset value thereby memorised.

Advantageously, for each second demodulation attempt, the sequenceformed by the samples thereby corrected is stripped of a given number ofits first samples, corresponding to a temporal offset, the strippedsequence is then cut up into blocks of given size and from each of saidblocks a given number of its first samples is eliminated, correspondingto an OFDM symbol prefix time.

For each block k=0, . . . ,K−1 where K is the total number of blocksobtained, a FFT may be calculated by:

${\hat{a}}_{k,n} = {\sum\limits_{p = 0}^{\beta_{0} - 1}\;{\rho_{p}^{k}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta_{0}}}}}$where β₀ is the memorised useful time value, expressed in number ofsamples, T_(e) is the sampling period, ρ_(p) ^(k) is the (p+1)^(ième)frequency corrected sample of the k^(ième) block and the â_(k,n), k=0, .. . ,K−1, n=0, . . . ,{circumflex over (N)}−1, form a sequence ofdemodulated symbols according to said second demodulation attempt.

A second value (Φ(δ,γ)) of said cost function is then calculated fromsaid sequence of demodulated symbols.

Advantageously, said cost function is the kurtosis.

In this case, the value of said cost function is calculated by:

${\Phi\left( {\delta,\gamma} \right)} = {{\hat{\kappa}\left( \left\{ {\hat{a}}_{k,n} \right\} \right)} = {\frac{\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{4}}}{\left( {\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}} - 2 - \frac{{{\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{k,n} \right)^{2}}}}^{2}}{\left( {\sum\limits_{k = 0}^{K - 1}\;{\sum\limits_{n = 0}^{\hat{N} - 1}\;{{\hat{a}}_{k,n}}^{2}}} \right)^{2}}}}$

The estimation method takes place advantageously in an iterative manner,each iteration corresponding to a second demodulation attempt by meansof memorised frequency offset and useful time values, of a said temporaloffset value and a said prefix time.

As the iterations proceed, a discrete temporal offset and prefix timeseries is preferably run through, according to a scanning algorithm, andthe temporal offset and prefix time values achieving the minimum of thecost function on said series is memorised, the estimation of the secondtime parameter being the prefix time thereby memorised.

Advantageously, the scanning algorithm is of gradient descent type.

BRIEF DESCRIPTION OF DRAWINGS

Other characteristics and advantages of the invention will become clearon reading a preferential embodiment of the invention and by referringto the appended figures in which:

FIG. 1 illustrates in a schematic manner an OFDM signal;

FIG. 2 illustrates in a schematic manner an OFDM receiver known to theprior art;

FIGS. 3A and 3B represent the respective contributions of the differentpaths to the OFDM signal received by a receiver;

FIG. 4 gives a block diagram of the estimation method of OFDM modulationparameters according to a first embodiment of the invention;

FIGS. 5A and 5B give a block diagram of the estimation method of OFDMmodulation parameters according to a second embodiment of the invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

The case of a telecommunications system using an OFDM modulation will beconsidered hereafter. It will be assumed that the OFDM signal emittedhas the form given by the expression (1) and that the informationsymbols may be represented by independent random variables, identicallydistributed and taking their values in a M-ary modulation alphabet. TheOFDM symbols may contain or not a prefix. With a view to simplification,it will be considered that they contain a prefix but that this prefixmay be empty.

It will be assumed that the transmission channel is of multi-path type.The signal received by the receiver may then be expressed, in baseband,by:

$\begin{matrix}{{r_{a}(t)} = {{\sum\limits_{l = 1}^{L}\;{\lambda_{j}{s_{a}\left( {t - \tau_{l}} \right)}}} = {b(t)}}} & (4)\end{matrix}$where the λ_(l) and τ_(l) are respectively the complex attenuationcoefficients and the delays associated with the different paths, L isthe total number of paths and b(t) an additive white Gaussian noise.

We will now place ourselves in a blind context, in other words thereceiver does not know the modulation parameters of the OFDM signal, inparticular the chip frequency of the signal.

The signal received is sampled at a frequency

$f_{e} = \frac{1}{T_{e}}$greater than the Nyquist frequency. One is therefore certain that thesampling period T_(e) is less than the chip period T_(c).

If it assumed firstly that the receiver is perfectly synchronisedtemporally and frequentially, the samples of signal received may beexpressed in the following manner:

$\quad\begin{matrix}\begin{matrix}{\forall{p \in \left\lbrack {0,{\hat{P} - {1\left\lbrack {r_{k,p} = {r_{a}\left( {{pT}_{e} + {\overset{\bullet}{D}T_{c}} + {k\left( {{\overset{\bullet}{N}T_{c}} + {\overset{\bullet}{D}T_{c}}} \right)}} \right)}} \right.}}} \right.}} \\{= {\sum\limits_{l = 1}^{L}{\lambda_{l}{s_{a}\left( {{pT}_{e} + {\overset{\bullet}{D}T_{c}} +} \right.}}}} \\\left. {{k\left( {{\overset{\bullet}{N}T_{c}} + {\overset{\bullet}{D}T_{c}}} \right)} - \tau_{l}} \right)\end{matrix} & (5)\end{matrix}$in which, in a first instance, the noise term has been disregarded,where k,p are respectively the symbol number and the rank of the samplewithin a symbol,

T_(c) is an estimation of the time of the prefix and where {circumflexover (P)} is a whole number such that

is minimal.

The samples of signal received are subject to a discrete Fouriertransform, to obtain the estimated demodulated symbols:

$\begin{matrix}{{\hat{a}}_{k,v} = {\sum\limits_{p = 0}^{\hat{P} - 1}{r_{k,p}{\mathbb{e}}^{2{\mathbb{i}\pi}\; p\frac{{vT}_{e}}{T_{c}}}}}} & (6)\end{matrix}$Consider firstly the decoded symbols of the first OFDM symbol, i.e.{â_(0,v)}_(v). By using the expression (5):

$\begin{matrix}{{\hat{a}}_{0,v} = {\sum\limits_{l = 1}^{L}{\sum\limits_{k \in \Omega_{l}}{\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{\overset{\sim}{a}}_{k,n}^{(l)}{\sum\limits_{p = 0}^{\hat{P} - 1}{{\mathbb{e}}^{{- 2}{\mathbb{i}\pi}\;{{pT}_{e}{({\frac{n}{{NT}_{c}} - \frac{v}{T_{c}}})}}}\lambda_{l}{g\left( {{pT}_{e} + {T_{c}} - \tau_{l} - {{k\left( {N + D} \right)}T_{c}}} \right)}}}}}}}}} & (7)\end{matrix}$where

 is an estimation of the useful time of the OFDM symbols;

${\overset{\sim}{a}}_{k,n}^{(l)} = {a_{k,n}{\mathbb{e}}^{{- 2}{\mathbb{i}\pi}\;{{n{({{T_{c}} - {DT}_{c} - \tau_{l} - {{k{({N + D})}}T_{c}}})}}/{NT}_{c}}}}$where a_(k,n) is the n^(th) sample of the block k transmitted;

-   Ω_(l) is the series of values k ε Z such that ∃p ε[0, {circumflex    over (P)}−1] such that g(pT_(e)+    −τ_(l)−k(N+D)T_(c))≠0. Without loss of generality, it will be    assumed hereafter that g=1_((N+D)T) _(c) _(′) window function equal    to 1 between 0 and (N+D)T_(c) and zero everywhere else.

Consider the contribution of a path on the decoded symbol. To do thisâ_(0,v) ^((l)) is introduced such that:

${\hat{a}}_{0,v}^{(l)} = {\sum\limits_{k \in \Omega_{l}}{\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{\overset{\sim}{a}}_{k,n}^{(l)}{\sum\limits_{p = 0}^{\hat{P} - 1}{{\mathbb{e}}^{{- 2}{\mathbb{i}\pi}\;{{pT}_{e}{({\frac{n}{{NT}_{c}} - \frac{v}{T_{c}}})}}}\lambda_{l}{g\left( {{pT}_{e} + {T_{c}} - \tau_{l} - {{k\left( {N + D} \right)}T_{c}}} \right)}}}}}}}$and thus:

$\begin{matrix}{{\hat{a}}_{0,v} = {\sum\limits_{l = 1}^{L}{\hat{a}}_{0,v}^{(l)}}} & (8)\end{matrix}$

If Card(Ω_(l))=1, it can be shown by making the hypothesis that N islarge ahead of 1 (which is the case for the very large majority of OFDMsystems) that:

$\begin{matrix}{{\hat{a}}_{0,v}^{(l)} = {\frac{\lambda_{l}}{N}{\sum\limits_{n = 0}^{N - 1}{{\overset{\sim}{a}}_{{k{(l)}},n}^{(l)}{\mathbb{e}}^{\mathbb{i}\theta}\frac{\sin\left( {\pi\frac{T_{c}}{{NT}_{c}}\left( {n - {v\frac{{NT}_{c}}{T_{c}}}} \right)} \right)}{\sin\left( {\pi\;{T_{e}\left( {n - {v\frac{{NT}_{c}}{T_{c}}}} \right)}} \right)}}}}} & (9)\end{matrix}$and that

${\hat{a}}_{0,v}^{(l)} = {\frac{\lambda_{l}}{{NT}_{e}}{\overset{\sim}{a}}_{{k{(l)}},v}^{(l)}{\mathbb{e}}^{\mathbb{i}\theta}}$if and only if

.

On the other hand, if Card(Ω_(l))>1, the decoded symbol â_(0,v) ^((l))always depends on at least two independent OFDM symbols.

By applying this result to the estimated symbol

${{\hat{a}}_{0,v} = {\sum\limits_{l = 1}^{L}{\hat{a}}_{0,v}^{(l)}}},$it may be deduced by expressing ã_(k(l),v) ^((l)) as a function ofa_(k(l),v) that:

$\begin{matrix}{{\hat{a}}_{0,v} = {a_{k,n}{\sum\limits_{l = 1}^{L}{\frac{\lambda_{l}}{{NT}_{e}}{\mathbb{e}}^{{- 2}{\mathbb{i}\pi}\;{{n{({{T_{c}} - {DT}_{c} - \tau_{l} - {{k{({N + D})}}T_{c}}})}}/{NT}_{c}}}{\mathbb{e}}^{{\mathbb{i}}\;\theta}}}}} & (10)\end{matrix}$if and only if, ∀l, k(l)=k.

It may be deduced from this first result that if the samples r_(0,p) aresamples of a same OFDM symbol, (the same for all the paths), then theestimated symbols â_(0,v) only depend on a single one of the transmittedsymbols, ã_(0,v) if and only if

=NT_(c). If not, in all other cases, â_(0,v) depends on at least two ofthe symbols transmitted

It will be noted that if the time of the cyclic prefix is longer thanthe length of the impulse response of the transmission channel, there isno intersymbol interference. More precisely, the useful part of an OFDMsymbol being propagated along a path is not interfered by another OFDMsymbol being propagated along another path.

In FIG. 3A is represented the OFDM signal 310 as emitted by the emitterand in 320, 330, 340, the contributions to the signal received,corresponding to the propagation of said OFDM signal along threeseparate paths. It will be noted that the useful part of an OFDM symbolpropagating on one path does not overlap another OFDM symbol propagatingon another path.

This result also holds for the other OFDM symbols, in other words fork>0. One deduces from this, that an estimated symbol â_(k,v), for any k,only depends on a single one of the symbols transmitted if and only if

. If this is not the case, it can be shown that the samples r_(k,p)correspond to samples of at least 2 OFDM symbols.

This result is illustrated in FIG. 3B, the OFDM signals being propagatedalong the three paths. In I is represented the case of an exact estimate

 but with an erroneous estimate

. It will be understood that two consecutive OFDM symbols then intervenein the calculation of â_(k,v) (the estimated useful part of width

 then covers the prefix of the following symbol). In other words,Card(Ω)=2. In the same way, in II is represented the case where theestimates

 and

 are exact. It will be seen that an OFDM symbol then intervenes in thecalculation of â_(μ,v).

An incorrect estimation of time parameter leads to Card(Ω)≧2 whichincreases the entropy of the demodulated signal compared to the casewhere one has an exact estimation (Card(Ω)=1).

The basic idea of the invention is to use a criterion of minimum entropyto determine whether the sampling boundaries are aligned on the startand the end of the useful part of an OFDM signal.

To do this, the signal sampled is demodulated by varying the modulationparameters and the parameter(s) leading to a minimum of entropy of thesignal thereby demodulated is(are) selected.

Indeed, if the sampling boundaries are well aligned on the start and theend of the useful part, the entropy of the demodulated sequence will beminimal. On the other hand, from the moment that these boundaries areoffset in relation to the limits of the useful part, the portion of OFDMsymbol preceding or following the current symbol will lead to anincrease in the entropy of the demodulated sequence.

In order to minimise the entropy, a cost function, representative of theentropy of the demodulated signal, for example the kurtosis of thissequence, is used.

It will be recalled that the kurtosis of a random variable is the ratiobetween its fourth order cumulant and the square of its variance. Moreprecisely, if α is a complex random variable, the kurtosis of α may bewritten as:

$\begin{matrix}{{\kappa(\alpha)} = {\frac{{cum}_{4}(\alpha)}{\left( {{cum}_{2}(\alpha)} \right)^{2}} = {\frac{E\left\{ {\alpha }^{4} \right\}}{\left( {E\left\{ {\alpha }^{2} \right\}} \right)^{2}} - 2 - \frac{{{E\left\{ \alpha^{2} \right\}}}^{2}}{\left( {E\left\{ {\alpha }^{2} \right\}} \right)^{2}}}}} & (11)\end{matrix}$where one has noted E{x} the mathematical expectation of x. If α_(n),n=0, . . . ,N−1 is a realisation of a sequence of N independent andidentically distributed (i.i.d.) random variables, the kurtosis of thesequence α is estimated by:

$\begin{matrix}{{\hat{\kappa}(\alpha)} = {\frac{\sum\limits_{n = 0}^{N - 1}{\alpha_{n}}^{4}}{\left( {\sum\limits_{n = 0}^{N - 1}{\alpha_{n}}^{2}} \right)^{2}} - 2 - \frac{{{\sum\limits_{n = 0}^{N - 1}\alpha_{n}^{2}}}^{2}}{\left( {\sum\limits_{n = 0}^{N - 1}{\alpha_{n}}^{2}} \right)^{2}}}} & (12)\end{matrix}$

It should be noted that the kurtosis of a random variable is also ameasurement of the difference between its probability density and aGaussian distribution. In particular, the kurtosis of a Gaussian randomvariable is zero.

Furthermore, it can be shown that the kurtosis has the followingimportant property, namely if:

$\begin{matrix}{x_{k} = {\sum\limits_{n = 0}^{N - 1}{\lambda_{k,n}a_{n}}}} & (13)\end{matrix}$where a_(n), n=0, . . . ,N−1 is a sequence of i.i.d. random variables,and the λ_(k,n), n=0, . . . ,N−1 are N complex coefficients, one has:κ(x _(k))≧min_(n)κ(a _(n))   (14)equality being only obtained if ∃n₀ ε {0, . . . N−1} such that:λ_(k,n) ₀ ≠0 et ∀n≠n₀λ_(k,n)=0   (15)where

$n_{0} = {\underset{n}{\arg\;\min}\;{{\kappa\left( a_{n} \right)}.}}$

If this property is applied to the estimated symbols â_(k,v), it may bederived that the kurtosis is minimal if and only if, ∀(k,v),â_(k,v) onlydepends on a single symbol emitted. Consequently, κ(â_(μ,v)) will beminimal and equal to κ(a_(k,n)) if and only if

 and

.

This may be understood intuitively in so far as an incorrect estimationof temporal parameters leads to â_(μ,v) estimates involving a greaternumber of i.i.d. random variables corresponding to the informationsymbols a_(k,n). In application of the central limit theorem, thekurtosis of â_(μ,v) then approaches that of a Gaussian random variable,i.e. tends towards zero by increasing values.

The presence of the Gaussian noise in (4) does not change in any way theprevious result. Indeed, if y(t)=s(t)+b(t) where b(t) is an additiveGaussian noise:

$\quad\begin{matrix}\begin{matrix}{{\kappa(y)} = \frac{{{cum}_{4}(s)} + {{cum}_{4}(b)}}{\left( {{E\left( {s}^{2} \right)} + \sigma_{b}^{2}} \right)^{2}}} \\{= \frac{{cum}_{4}(s)}{\left( {{E\left( {s}^{2} \right)} + \sigma_{b}^{2}} \right)^{2}}} \\{= {{\kappa(s)}\frac{E\left( {s}^{2} \right)}{\left( {{E\left( {s}^{2} \right)} + \sigma_{b}^{2}} \right)^{2}}}}\end{matrix} & (16)\end{matrix}$where one has noted cum₄(.) the fourth order cumulant and σ_(b) ² thenoise variance. Given that b is Gaussian, one has cum₄(b)=0. It ensuesfrom (16) that the kurtosis of y is proportional to the kurtosis of s.Consequently, the minimisation of the kurtosis of y leads tominimisation of the kurtosis of s and therefore to the correctestimation of the temporal parameters DT_(c) and NT_(c).

The previous result assumes that the receiver is temporally andfrequentially synchronised with the OFDM signal. If this is not thecase, the previous result remains nevertheless valid, thesynchronisation defect leading to an increase of the kurtosis of thesequence sampled.

The search for the temporal and/or frequential synchronisation may becarried out jointly or prior to the estimation of the modulationparameters of the OFDM signal.

FIG. 4 represents a block diagram of an estimation method of themodulation parameters of the OFDM signal, according to a firstembodiment of the invention.

In this embodiment, the search for the temporal and/or frequentialsynchronisation is carried out in the same optimisation loop as theestimation of the OFDM modulation parameters.

At step 410, after demodulation if necessary in base band of the signalreceived, a sampling is carried out at a frequency greater than theNyquist frequency, in other words with a sampling period T_(e) less thanthe chip period T_(c) of the OFDM signal emitted.

At step 420, one initialises the number of iterations m at 1 and a valueΦ_(min) at a high number. One then initialises the value of thefrequency offset Δf (or in an equivalent manner a phase valueΔφ=Δf.2πT_(e)) corresponding to the difference between the carrierfrequency of the OFDM multiplex and the demodulation frequency, thetemporal offset δ, expressed in number of samples, i.e. Δt=δ.T_(e) whereΔt determines the start of the sampling window of the OFDM signal. Onefinally initialises the values of the temporal parameters of modulation,expressed in number of samples, i.e. γ and β, such that

 and

. These values expressed in number of chip periods are noted {circumflexover (N)} and {circumflex over (D)}. It will be noted that {circumflexover (N)} is also the number of assumed carriers for the OFDM multiplex.One could in particular initialise {circumflex over (N)} at a low numberof carriers of an OFDM system, for example {circumflex over (N)}=64.

One then enters into an iterative loop aiming to search for the minimumentropy of the demodulated sequence. Advantageously, a functionrepresentative of the entropy of the demodulated sequence is used,preferably the kurtosis of this sequence. Each iteration of the loopcorresponds to a demodulation attempt of the OFDM signal by means of aquadruplet of different parameters, as explained hereafter.

At step 425, the samples received from the dephasing corresponding tosaid frequency offset are corrected Δf, i.e. ρ_(p)=r_(p)e^(ipΔφ).

At step 430, the δ first samples of the sequence thereby obtained areeliminated. The sampling window is thereby locked.

At step 435, the sequence sampled is cut up into blocks of size γ+β.I.e. K the number of full blocks thereby obtained. One notes ρ_(p) ^(k),p=0, . . . ,β−1 the samples of the k^(th) block.

At step 440, one eliminates from each of these K blocks obtained the γfirst samples, in other words those corresponding to the assumed prefix.

At step 445, a FFT of size β of the K blocks thereby obtained is thencarried out, i.e.:

$\begin{matrix}\begin{matrix}{{\hat{a}}_{k,n} = {\sum\limits_{p = 0}^{\beta - 1}{\rho_{p}^{k}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta}}}}} & {{\forall{k \in \left\lbrack {0,{K - 1}} \right\rbrack}};} & {\forall{n \in \left\lbrack {0,{\hat{N} - 1}} \right\rbrack}}\end{matrix} & (17)\end{matrix}$

In 450, the value of the cost function, noted Φ is calculated fromdemodulated symbols. Obviously, this value depends on the choice of thetemporal and frequential offset values, as well as the modulationparameters, i.e. Φ(Δφ,δ,γ,β). If the cost function used is the kurtosisκ:

$\begin{matrix}\begin{matrix}{{\Phi\left( {{\Delta\varphi},\delta,\gamma,\beta} \right)} = {\hat{\kappa}\left( \left\{ {\hat{a}}_{k,n} \right\} \right)}} \\{= {\frac{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{4}}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}} - 2 - \frac{{{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{k,n} \right)^{2}}}}^{2}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}}}}\end{matrix} & (18)\end{matrix}$

In 455, one compares the value Φ(Δφ,δ,γ,β) to Φ_(min).

If Φ(Δφ,δ,γ,β)<Φ_(min), the minimal value Φ_(min) is updated in 457 bymeans of Φ_(min)=Φ(Δφ,δ,γ,β) and the corresponding current values arestored Δφ,δ,γ,β.

In all cases, one goes through step 460. One compares m with apredetermined maximal number of iterations M. If this maximal number isattained, the algorithm is terminated in 465. If not, one moves ontostep 470.

In 470, the counter m of iterations is incremented, the values ofΔφ,δ,γ,β are updated according to a scanning plan. For example, each ofthe variables Δφ,δ,γ,β will be authorised to take a series of discretevalues within a predetermined respective intervalI_(Δφ),I_(δ),I_(γ),I_(β), the scanning then being carried out within afour dimensional space within the volume I_(Δφ)×I_(δ)×I_(γ)×I_(β). Thescanning may be systematic and predefined. One could however useadvantageously an algorithm of the gradient descent type to update ateach iteration the values of Δφ,δ,γ,β. After the updating of thevariables one returns to step 425 for a new demodulation attempt.

At the end of the scanning, in other words in 465, when the number M ofiterations is attained, the parameters Δφ₀,δ₀,γ₀,β₀ making the valueΦ_(min) are then used to demodulate the OFDM signal, namely:

$\begin{matrix}{{{f} = \frac{{\Delta\varphi}_{0}}{2\pi\; T_{e}}};{{t} = {\delta_{0} \cdot T_{e}}};{{T_{c}} = {\gamma_{0}T_{e}}};{{T_{c}} = {\beta_{0}T_{e}}};} & (19)\end{matrix}$

It will be noted that this algorithm makes it possible to obtain asynchronisation at the end of a low number of OFDM symbols as well as anacquisition just as rapid of the temporal parameters of modulation OFDM.

Once the demodulation has been obtained by means of the parameters (19),the equalisation of the demodulated symbols may be carried out, in amanner known to those skilled in the art to estimate the informationsymbols.

In order to further reduce the acquisition time, it is possible toproceed in two stages, by performing a first rough estimation of thesynchronisation parameters and a modulation parameter, then byperforming a finer estimation of the temporal offset and the othermodulation parameter.

FIG. 5A and FIG. 5B represent a block diagram of an estimation method ofthe temporal parameters of modulation of an OFDM signal, according to asecond embodiment of the invention.

In this embodiment, in a first loop a rough synchronisation search on asingle OFDM symbol is carried out.

Step 510 is identical to step 410, the signal received is sampled at afrequency greater than that of Nyquist, after demodulation if necessaryin baseband.

At step 520, one initialises the number of iterations m₁ at 1 and avalue Φ_(min) at a high number. The value of the frequency offset Δf (orin an equivalent manner a phase value Δφ=Δf.2πT_(e)), the temporaloffset value δ, expressed in number of samples as well as the prefixtime, expressed in number of samples, β, are then initialised.

At step 525, the received samples are corrected from the phase offsetscorresponding to the frequency offset Δf, i.e. ρ_(p)=r_(p)e^(ipΔφ).

At step 530, the δ first samples of the sequence thereby obtained areremoved.

At step 535, the sequence obtained after β samples is truncated and, in540 a FFT of size β on these samples is then carried out, i.e.:

$\begin{matrix}\begin{matrix}{{\hat{a}}_{n} = {\sum\limits_{p = 0}^{\beta - 1}{\rho_{p}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta}}}}} & {\forall{n \in \left\lbrack {0,{\hat{N} - 1}} \right\rbrack}}\end{matrix} & (20)\end{matrix}$where the samples of the previously truncated sequence have been notedρ_(p), p=0, . . . ,β−1.

At step 540, the value of the entropic cost function Φ is calculatedfrom the demodulated symbols. This value depends on the temporal andfrequential offset values, as well as the parameter β, i.e. Φ(Δφ,δ,β).If the cost function used is the kurtosis κ, one simply has:

$\begin{matrix}{{\Phi\left( {{\Delta\varphi},\delta,\beta} \right)} = {{\hat{\kappa}\left( \left\{ {\hat{a}}_{n} \right\} \right)} = {\frac{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{4}}{\left( {\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{2}} \right)^{2}} - 2 - \frac{{{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{n} \right)^{2}}}^{2}}{\left( {\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{2}} \right)^{2}}}}} & (21)\end{matrix}$

At step 545, one compares the value Φ(Δφ,δ,β) to Φ_(min).

If Φ(Δφ,δ,β)<Φ_(min), the minimal value Φ_(min) is updated in 547 bymeans of Φ_(min)=Φ(Δφ,δ,β) and the corresponding current values arestored Δφ,δ,β.

In all cases, one goes through step 550. One compares m₁ with a maximalpredetermined number of iterations M₁. If this maximal number isattained, one moves onto step 555. If not, in 557, the values of Δφ,δ,βare updated according to a scanning algorithm. This algorithm may besystematic by scanning according to a pre-established order of discretevalues in a volume I_(Δφ)×I_(δ)×I_(β), or even be adaptive, for exampleof the gradient descent type. After updating the values Δφ,δ,β, onereturns to step 525.

At step 555, one memorises the values Δφ₀,δ₀,β₀ making Φ_(min). Theycorrespond to an estimation of the frequential and temporal offsets aswell as the useful length of the OFDM symbols:

$\begin{matrix}\begin{matrix}{{{f} = \frac{{\Delta\varphi}_{0}}{2\pi\; T_{e}}};} & {{{t} = {\delta_{0} \cdot T_{e}}};} & {{T_{c}} = {\beta_{0}T_{e}}}\end{matrix} & (22)\end{matrix}$

One then uses these values to initialise the second iteration loop. Moreprecisely:

One initialises, in 557, the counter of iterations, m₂, at 1, δ at thevalue δ₀, as well as the time of the prefix, expressed in number ofsamples, γ.

At step 560, the samples received from the dephasing corresponding tothe frequency offset

f are corrected, i.e. ρ_(p)=r_(p)e^(ipΔφ) ⁰ .

One enters into the second iteration loop at step 565. In 565, δ firstsamples of the sequence thereby obtained are eliminated.

At step 570, the sequence sampled is cut up into blocks of size γ+β₀. Kdenotes the number of full blocks thereby obtained. ρ_(p) ^(k), p=0, . .. ,β₀−1 denote the samples of the k^(th) block.

In 575, one eliminates from each of these K blocks obtained the γ firstsamples, in other words those assumed to belong to the prefix.

At step 580, a FFT of size β₀ of the K blocks thereby obtained isperformed, i.e.:

$\begin{matrix}\begin{matrix}\begin{matrix}{{\hat{a}}_{k,n} = {\sum\limits_{p = 0}^{\beta_{0} - 1}{\rho_{p}^{k}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta_{0}}}}}} & {{\forall{k \in \left\lbrack {0,{K - 1}} \right\rbrack}};}\end{matrix} & {\forall{n \in \left\lbrack {0,{\hat{N} - 1}} \right\rbrack}}\end{matrix} & (23)\end{matrix}$

In 585, the value of the cost function is calculated from thedemodulated symbols. This value depends on the choice of the temporaloffset value as well as the parameter γ, i.e. Φ(δ,γ) since

and

 are respectively fixed at

$\frac{{\Delta\varphi}_{0}}{2\pi\; T_{e}}\mspace{11mu}{and}\mspace{14mu}\beta_{0}{T_{e}.}$If the cost function used is the kurtosis κ:

$\begin{matrix}{{\Phi\left( {\delta,\gamma} \right)} = {{\hat{\kappa}\left( \left\{ {\hat{a}}_{k,n} \right\} \right)} = {\frac{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{4}}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}} - 2 - \frac{{{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{k,n} \right)^{2}}}}^{2}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}}}}} & (24)\end{matrix}$

At step 587, one compares the value Φ(δ,γ) to Φ_(min).

If Φ(δ,γ)<Φ_(min), the minimal value Φ_(min) is updated in 590 byΦ_(min)= (δ,γ) and the corresponding values δ,γ are stored.

At step 593, one compares m₂ with a maximal predetermined number ofiterations M₂. If this maximal number is attained, 595 is terminated. Ifnot, one moves onto step 597.

In 597, the counter m₂ of iterations is incremented, the values of δ,γare updated according to the same principle as previously. After theupdating of the variables, one returns to step 5 for a new demodulationattempt.

At the end of the scanning, in other words in 593, when the number M₂ ofiterations is attained, the parameters δ₁,γ₁ making the value Φ_(min)are then used to demodulate the OFDM signal. Finally, the demodulatorthus uses the parameters:

$\begin{matrix}\begin{matrix}{{{f} = \frac{{\Delta\varphi}_{0}}{2\pi\; T_{e}}};} & {{{t} = {\delta_{1} \cdot T_{e}}};} & {{{T_{c}} = {\gamma_{1}T_{e}}};} & {{{T_{c}} = {\beta_{0}T_{e}}};}\end{matrix} & (25)\end{matrix}$

According to this embodiment, the first loop enables the estimation ofthe useful time of the symbol and the second loop that of the durationof the prefix. Alternatively, the first loop may enable the estimationof the duration of the prefix, and the second loop that of the time ofthe useful part.

In all cases, after the demodulation obtained by means of the parameters(25), the equalisation of the demodulated symbols may be carried out, ina manner known to those skilled in the art, in order to estimate theinformation symbols.

1. A blind estimation method of at least one temporal modulationparameter of an orthogonal frequency division multiplex (OFDM) signal,said temporal modulation parameter being a useful time, a guardinterval, or a repetition period of OFDM symbols of said OFDM signal,wherein: a plurality of demodulation attempts of said OFDM signal arecarried out using a plurality of respective values of the temporalparameter, the OFDM signal being demodulated in base band by means of ademodulation frequency, then sampled at a frequency greater than aNyquist frequency to obtain a sequence of samples; said samples arecorrected by a phase offset (Δφ) corresponding to a frequency offsetvalue (Δf) between a carrier frequency of an OFDM multiplex of the OFDMsignal and the demodulation frequency; and, for each demodulationattempt, a cost function representative of the entropy of thedemodulated signal is calculated, an estimate of said temporal parameterbeing obtained as a value of this parameter minimising said costfunction.
 2. The estimation method according to claim 1, characterisedin that, for each demodulation attempt, the sequence formed by thesamples thereby corrected is stripped of a given number (δ) of its firstsamples, corresponding to a temporal offset.
 3. The estimation methodaccording to claim 2, characterised in that, for each demodulationattempt, the sequence thus stripped is cut up into blocks of given size(γ+β), that each of the blocks thereby obtained is stripped of a givennumber (γ) of its first samples, corresponding to an OFDM symbol prefixtime, and that a FFT of each of the blocks thus stripped is performed.4. The estimation method according to claim 3, characterised in that,for each block k=0, . . . ,K−1 where K is the total number of blocks ofthe stripped sequence, the FFT is calculated by:${\hat{a}}_{k,n} = {\sum\limits_{p = 0}^{\beta - 1}{\rho_{p}^{k}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta}}}}$where β is the size of the stripped blocks, corresponding to an OFDMsymbol useful time, T_(e) is the sampling period, ρ_(p) ^(k) is the(p+1)^(th) frequency corrected sample of the k^(th) block and theâ_(k,n), k=0, . . , K−1, n=0, . . . , {circumflex over (N)}−1 where{circumflex over (N)} is said useful time expressed in chip periods,form a sequence of demodulated symbols according to said demodulationattempt.
 5. The estimation method according to claim 4, characterised inthat the value of said cost function is calculated from said sequence ofdemodulated symbols.
 6. The estimation method according to claim 1,characterised in that said cost function is the kurtosis.
 7. Theestimation method according to claim 5, characterised in that the valueof said cost function is calculated by:${\hat{\kappa}\left( \left\{ {\hat{a}}_{k,n} \right\} \right)} = {\frac{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{4}}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}} - 2 - \frac{{{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{k,n} \right)^{2}}}}^{2}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}}}$8. The estimation method according to claim 4, characterised in that itis carried out in an iterative manner, each iteration corresponding to ademodulation attempt by means of said frequency offset value, a temporaloffset value, said prefix time and said useful time.
 9. The estimationmethod according to claim 8, characterised in that as the iterationsproceed, a discrete series of frequency offset, temporal offset, prefixtime and useful time values are run through, according to a scanningalgorithm, and that as estimate(s) of the temporal parameter(s), theprefix time and/or the useful time achieving the minimum of the costfunction on said series is(are) retained.
 10. The estimation methodaccording to claim 9, characterised in that said scanning algorithm isof gradient descent type.
 11. The estimation method according to claim1, characterised in that one carries out a plurality of demodulationattempts, hereinafter referred to as first modulation attempts, toestimate a first time parameter, then a plurality of second demodulationattempts, hereinafter referred to as second modulation attempts, toestimate a second time parameter, said second demodulation attemptsusing the estimate of the first time parameter to demodulate the OFDMsignal.
 12. The estimation method according to claim 11, characterisedin that, for each first demodulation attempt, the samples are correctedby the phase offset (Δφ) corresponding to the frequency offset value(Δf) between the carrier frequency of the OFDM multiplex and thedemodulation frequency.
 13. The estimation method according to claim 12,characterised in that, for each first demodulation attempt, the sequencethus stripped is truncated after a given number of samples, said numbercorresponding to one given OFDM symbol useful time, then a FFT isperformed on the samples of the sequence thereby truncated.
 14. Theestimation method according to claim 13, characterised in that the FFTis calculated by:${\hat{a}}_{n} = {\sum\limits_{p = 0}^{\beta - 1}{\rho_{p}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta}}}}$where β is the length of the truncated sequence, T_(e) is the samplingperiod, ρ_(p) is the (p+1)^(th) frequency corrected sample of thetruncated sequence, the â_(n), n=0, . . . , {circumflex over (N)}−1,where {circumflex over (N)} is said useful time expressed in chipperiods, forming a sequence of demodulated symbols according to saidfirst demodulation attempt.
 15. The estimation method according to claim14, characterised in that a first value (Φ(Δφ,δ,β)) of said costfunction is calculated from said sequence of demodulated symbols. 16.The estimation method according to claim 11, characterised in that saidcost function is the kurtosis.
 17. The estimation method according toclaim 15, characterised in that the value of said cost function iscalculated by:${\hat{\kappa}\left( \left\{ {\hat{a}}_{n} \right\} \right)} = {\frac{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{4}}{\left( {\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{2}} \right)^{2}} - 2 - \frac{{{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{n} \right)^{2}}}^{2}}{\left( {\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{n}}^{2}} \right)^{2}}}$18. The estimation method according to claim 14, characterised in thatit is carried out in an iterative manner, each iteration correspondingto a first demodulation attempt by means of said frequency offset value,a temporal offset value, a prefix time and said useful time.
 19. Theestimation method according to claim 18, characterised in that, as theiterations proceed, a discrete series of frequency offset, temporaloffset, prefix time and useful time values are run through, according toa scanning algorithm, and that the frequency offset, temporal offset anduseful time values achieving the minimum of the cost function on saidseries is memorised, the estimation of the first time parameter beingthe useful time thereby memorised.
 20. The estimation method accordingto claim 19, characterised in that, each sample of said sequence ofsamples is corrected by a phase offset (Δφ₀) corresponding to thefrequency offset value (Δf) thereby memorised.
 21. The estimation methodaccording to claim 20, characterised in that, for each seconddemodulation attempt, the sequence formed by the samples therebycorrected is stripped of a given number of its first samples,corresponding to a temporal offset, the stripped sequence is cut up intoblocks of given size (γ+β₀) and from each of said blocks a given numberof its first samples are removed, corresponding to an OFDM symbol prefixtime.
 22. The estimation method according to claim 21, characterised inthat, for each block k=0, . . . , K−1 where K is the total number ofblocks obtained, a FFT is calculated by:${\hat{a}}_{k,n} = {\sum\limits_{p = 0}^{\beta_{0} - 1}{\rho_{p}^{k}{\mathbb{e}}^{2{\mathbb{i}\pi}\frac{np}{\beta_{0}}}}}$where β₀ is the value of useful time memorised, expressed in number ofsamples, T_(e) is the sampling period, ρ_(p) ^(k) is the (p+1)^(th)frequency corrected sample of the k^(th) block and the â_(k,n), k=0, . .. , K−1, n=0, . . . , {circumflex over (N)}−1, form a sequence ofdemodulated symbols according to said second demodulation attempt. 23.The estimation method according to claim 22, characterised in that asecond value(Φ(δ,γ)) of said cost function is calculated from saidsequence of demodulated symbols.
 24. The estimation method according toclaim 23, characterised in that said cost function is the kurtosis. 25.The estimation method according to claim 24, characterised in that thevalue of said cost function is calculated by:${\Phi\left( {\delta,\gamma} \right)} = {{\hat{\kappa}\left( \left\{ {\hat{a}}_{k,n} \right\} \right)} = {\frac{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{4}}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}} - 2 - {\frac{{{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}\left( {\hat{a}}_{k,n} \right)^{2}}}}^{2}}{\left( {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{n = 0}^{\hat{N} - 1}{{\hat{a}}_{k,n}}^{2}}} \right)^{2}}.}}}$26. The estimation method according to claim 25, characterised in thatit is carried out in an iterative manner, each iteration correspondingto a second demodulation attempt by means of the memorised frequencyoffset and useful time values, said temporal offset value and saidprefix time.
 27. The estimation method according to claim 26,characterised in that, as the iterations proceed, a series of temporaloffset and prefix time values is run through, according to a scanningalgorithm, and that the temporal offset and prefix time values achievingthe minimum of the cost function on said series is memorised, theestimation of the second time parameter being the prefix time therebymemorised.
 28. The estimation method according to claim 19,characterised in that the scanning algorithm is of gradient descenttype.